Hi I prove the first part of this problem but I don't know how to show the last part,
8.13. Suppose $l(D) >0 $, and let $f\ne 0$, $f\in l(D)$. Show that $f \notin L(D- P)$ for all but a finite number of $P$. So $l(D- P)=l(D)-1 $ for all but a finite number of $P$.
I don't understand how to get $l(D-P) = l(D) -1$,
Steps
The inequality that is notable is the following from what we prove: there exists an $ f$ in $L(D)/L(D-P)$, Furthermore, it is not difficult to show that if f is in $L(D-P)$ it is in $L(D)$ then we will have that $l(D-P) < l(D)$ then $l(D-P) \le l(D) -1$ but how could I show the other inequality?
From proposition $3$ in the same chapter of the exercise you know: $l(D)-l(D-P)\leq deg(D-(D-P))=1$.